A multiple choice exam has 50 questions with 5 choices for each question.If an individual is simply guessing at each answer, what are the values for the mean and the standard deviation of the normal approximation to the binomial distribution for the number of correct answers?
A) $ \mu=10 $ and $ \sigma=\sqrt{8} $
B) $ \mu=25 $ and $ \sigma=\sqrt{8} $
C) $ \mu=10 $ and $ \sigma=16 $
D) $ \mu=25 $ and $ \sigma=8 $

Question

A multiple choice exam has 50 questions with 5 choices for each question.If an individual is simply guessing at each answer, what are the values for the mean and the standard deviation of the normal approximation to the binomial distribution for the number of correct answers? 
A) $ \mu=10 $ and $ \sigma=\sqrt{8} $
B) $ \mu=25 $ and $ \sigma=\sqrt{8} $
C) $ \mu=10 $ and $ \sigma=16 $
D) $ \mu=25 $ and $ \sigma=8 $

Quizplus · Accepted Answer

The mean of a binomial distribution is $np$, where $n$ is the number of trials and $p$ is the probability of success on each trial. In this case, $n=50$ and $p=1/5$, so the mean is $np=50(1/5)=10$. The standard deviation of a binomial distribution is $\sqrt{npq}$, where $q=1-p$. In this case, $q=4/5$, so the standard deviation is $\sqrt{npq}=\sqrt{50(1/5)(4/5)}=\sqrt{8}$.

A Multiple Choice Exam Has 50 Questions with 5 Choices μ=10 \mu=10 μ=10

A Multiple Choice Exam Has 50 Questions with 5 Choices $\mu=10$